Abstract: We considered the asymptotic behavior of the heat equation on a semi infinite cylinder under nonstandard boundary conditions, where the solution satisfied the homogeneous Neumann condition in the local region on the side and the non-homogeneous Neumann condition in the other regions. Using the energy analysis method,  we obtained the spatial asymptotic theorem of the solution of the equation, and extended  results to the heat equation in binary mixtures.

Key words: heat equation, alternative, energy analysis, infinite cylinder